Description
A warehouse can store limited units of a commodity. Given an initial stock, the manager has to decide when to buy or sell in order to minimize total cost.
Small Model of Type : LP
Category : GAMS Model library
Main file : whouse.gms
$title Simple Warehouse Problem (WHOUSE,SEQ=4)
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A warehouse can store limited units of a commodity. Given an
initial stock, the manager has to decide when to buy or sell in
order to minimize total cost.
Dantzig, G B, Chapter 3.6. In Linear Programming and Extensions.
Princeton University Press, Princeton, New Jersey, 1963.
Keywords: linear programming, warehouse management, inventory
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Set t 'time in quarters' / q-1*q-4 /;
Parameter
price(t) 'selling price ($ per unit)' / q-1 10, q-2 12, q-3 8, q-4 9 /
istock(t) 'initial stock (units)' / q-1 50 /;
Scalar
storecost 'storage cost ($ per quarter per unit)' / 1 /
storecap 'stocking capacity of warehouse (units)' / 100 /;
Variable
stock(t) 'stock stored at time t (units)'
sell(t) 'stock sold at time t (units)'
buy(t) 'stock bought at time t (units)'
cost 'total cost ($)';
Positive Variable stock, sell, buy;
Equation
sb(t) 'stock balance at time t (units)'
at 'accounting: total cost ($)';
sb(t).. stock(t) =e= stock(t-1) + buy(t) - sell(t) + istock(t);
at.. cost =e= sum(t, price(t)*(buy(t) - sell(t)) + storecost*stock(t));
stock.up(t) = storecap;
Model swp 'simple warehouse problem' / all /;
solve swp minimizing cost using lp;